
A paint roller is a paint application tool used for painting large flat surfaces rapidly and efficiently. One such roller is shown below, which is long with an outer diameter of .

Find the maximum area of the surface that gets painted when the roller makes complete rotations vertically. Show your work. (Note: Take )


Important Questions on Surface Areas and Volumes
A container with a grey hemispherical lid has radius . In figure , it contains water up to a height of . It is then inverted as shown in figure .
What is the height of water in figure ?

Anishka melted chocolate cubes in a cylindrical cup as shown.
If the length of the side of each cube is and the radius of the cup is , which of these represents the height of the melted chocolate in the cup? (Note: Take )

Figure below is a solid cuboid made of unit cubes. Figure is obtained after removing some unit cubes from figure .
Based on the figures shown above, the surface area of the cuboid in figure is _____ the surface area of the solid in figure .

Water is supplied to a village through a water tanker.
The water tanker is cylindrical in shape with diameter and height . A total of litres of water is supplied through the tanker.
How many times was the water tanker used? (The tanker was always used at full capacity.) (Use and litres)

A tent is in the shape of a right circular cylinder up to a height of and conical above it. The total height of the tent is and the radius of its base is . Find the cost of cloth required to make the tent at the rate of per square meter [Take ]
If the required answer is , what is the value of ?

Shown below is a “spherical ring". A spherical ring is a sphere with a cylindrical hole drilled through it in such a way that the centres of the cylindrical hole and the sphere coincide. The radius of the spherical ring is and the length of hole drilled is .
The curved surface area of the spherical cap (part shaded in yellow in the figure) of height , is , where is the radius of the spherical ring.
The surface area of the ring is _____sq cm.
(Note: Use and round your answer to the nearest whole number.)


